Tsinghua University Bootcamp: Update

Misc/Tsinghua University Bootcamp in Summer 2024/Tsinghua Bootcamp 2024. Day 4/G.cpp

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+/**
+ * @file G.cpp
+ * @author Macesuted (i@macesuted.moe)
+ * @date 2024-08-26
+ *
+ * @copyright Copyright (c) 2024
+ *
+ */
+
+#include <bits/stdc++.h>
+using namespace std;
+
+#define endl '\n'
+#define maxn 200005
+
+class UnionSet {
+   private:
+    int fa[maxn], siz[maxn];
+    int64_t sum;
+
+    int getfa(int p) { return fa[p] == p ? p : fa[p] = getfa(fa[p]); }
+    int64_t calc(int64_t v) { return v * (v - 1) / 2; }
+
+   public:
+    void resize(int n) {
+        for (int i = 1; i <= n; i++) fa[i] = i, siz[i] = 1;
+        sum = 0;
+        return;
+    }
+    void merge(int x, int y) {
+        x = getfa(x), y = getfa(y);
+        if (x == y) return;
+        sum -= calc(siz[x]) + calc(siz[y]);
+        siz[x] += siz[y], fa[y] = x;
+        sum += calc(siz[x]);
+        return;
+    }
+    int64_t query(void) { return sum; }
+} US;
+
+set<int> S;
+int a[maxn], pos[maxn], n, k;
+
+void insert(int v) {
+    auto p = S.insert(v).first, pl = prev(p), pr = next(p);
+    if (*pl != 0 && *p - *pl <= k) US.merge(*p, *pl);
+    if (*pr != n + 1 && *pr - *p <= k) US.merge(*p, *pr);
+    return;
+}
+
+void solve(void) {
+    cin >> n >> k;
+    for (int i = 1; i <= n; i++) cin >> a[i], pos[i] = i;
+    US.resize(n);
+    sort(pos + 1, pos + n + 1, [&](int x, int y) { return a[x] > a[y]; });
+    S.insert(0), S.insert(n + 1);
+    int64_t lst = 0, ans = 0;
+    for (int i = 1; i <= n; i++) ans += a[i];
+    for (int i = 1; i <= n; i++) insert(pos[i]), ans += a[pos[i]] * (US.query() - lst), lst = US.query();
+    cout << ans << endl;
+    return;
+}
+
+int main() {
+    ios::sync_with_stdio(false), cin.tie(nullptr), cout.tie(nullptr);
+
+    int _ = 1;
+    while (_--) solve();
+
+    return 0;
+}

Misc/Tsinghua University Bootcamp in Summer 2024/Tsinghua Bootcamp 2024. Day 4/K.cpp

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+/**
+ * @file K.cpp
+ * @author Macesuted (i@macesuted.moe)
+ * @date 2024-08-26
+ *
+ * @copyright Copyright (c) 2024
+ *
+ */
+
+#include <bits/stdc++.h>
+using namespace std;
+
+#define endl '\n'
+#define maxn 1005
+#define maxm 10005
+
+typedef pair<int, int> pii;
+
+bool f[maxn][maxn];
+int rest[maxn][maxn], cur[maxn][maxn];
+pii h[maxm];
+
+bool solve(void) {
+    int n, k, m;
+    cin >> n >> k >> m;
+    if (k <= 2) return true;
+    if (k == 4) return m == 1;
+    for (int i = 1; i <= m; i++) cin >> h[i].first >> h[i].second;
+    sort(h + 1, h + m + 1);
+    f[n][n] = true;
+    for (int i = n; i; i--)
+        for (int j = n; j; j--) {
+            if (!f[i][j]) continue;
+            if (!rest[i][j]) rest[i][j] = h[++cur[i][j]].second;
+            if (rest[i][j] >= i) f[i][j - 1] = true, rest[i][j - 1] = rest[i][j] - i, cur[i][j - 1] = cur[i][j];
+            if (rest[i][j] >= j) f[i - 1][j] = true, rest[i - 1][j] = rest[i][j] - j, cur[i - 1][j] = cur[i][j];
+        }
+    for (int i = 1; i <= n; i++)
+        if (f[i][0] || f[0][i]) return true;
+    return false;
+}
+
+int main() {
+    ios::sync_with_stdio(false), cin.tie(nullptr), cout.tie(nullptr);
+
+    int _ = 1;
+    while (_--) cout << (solve() ? "YES" : "NO") << endl;
+
+    return 0;
+}

Misc/Tsinghua University Bootcamp in Summer 2024/Tsinghua Bootcamp 2024. Day 4/L.cpp

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+/**
+ * @file L.cpp
+ * @author Macesuted (i@macesuted.moe)
+ * @date 2024-08-26
+ *
+ * @copyright Copyright (c) 2024
+ *
+ */
+
+#include <bits/stdc++.h>
+using namespace std;
+
+#define endl '\n'
+#define maxn 20
+
+int64_t a[maxn][maxn], b[maxn], Sl[1024], Sr[1024];
+
+void solve(void) {
+    int n, m;
+    int64_t s;
+    cin >> n >> m;
+    for (int i = 0; i < n; i++)
+        for (int j = 0; j < m; j++) cin >> a[i][j];
+    cin >> s;
+    int tm = m / 2, om = m - tm;
+    for (int S = 0; S < (1 << n); S++) {
+        for (int j = 0; j < m; j++) b[j] = 0;
+        for (int j = 0; j < (1 << tm); j++) Sl[j] = 0;
+        for (int j = 0; j < (1 << om); j++) Sr[j] = 0;
+        for (int i = 0; i < n; i++)
+            if (S >> i & 1)
+                for (int j = 0; j < m; j++) b[j] += a[i][j];
+        for (int j = 0; j < tm; j++) Sl[1 << j] = b[j];
+        for (int j = 0; j < om; j++) Sr[1 << j] = b[tm + j];
+        unordered_map<int64_t, int> St;
+        for (int T = 0; T < (1 << tm); T++) {
+            if (T) {
+                int lb = T & -T;
+                Sl[T] = Sl[lb] + Sl[T ^ lb];
+            }
+            St[Sl[T]] = T;
+        }
+        for (int T = 0; T < (1 << om); T++) {
+            if (T) {
+                int lb = T & -T;
+                Sr[T] = Sr[lb] + Sr[T ^ lb];
+            }
+            if (St.count(s - Sr[T])) {
+                int64_t rT = St[s - Sr[T]] | (T << tm);
+                cout << "YES" << endl;
+                vector<pair<int, int>> ans;
+                for (int i = 0; i < n; i++)
+                    if (!(S >> i & 1)) ans.emplace_back(1, i + 1);
+                for (int j = 0; j < m; j++)
+                    if (!(rT >> j & 1)) ans.emplace_back(2, j + 1);
+                cout << ans.size() << endl;
+                for (auto [x, y] : ans) cout << x << ' ' << y << endl;
+                return;
+            }
+        }
+    }
+    cout << "NO" << endl;
+    return;
+}
+
+int main() {
+    ios::sync_with_stdio(false), cin.tie(nullptr), cout.tie(nullptr);
+
+    int _ = 1;
+    while (_--) solve();
+
+    return 0;
+}

Misc/Tsinghua University Bootcamp in Summer 2024/Tsinghua Bootcamp. Finals/A.cpp

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+/**
+ * @file A.cpp
+ * @author Macesuted (i@macesuted.moe)
+ * @date 2024-08-26
+ *
+ * @copyright Copyright (c) 2024
+ *
+ */
+
+#include <bits/stdc++.h>
+using namespace std;
+
+#define endl '\n'
+
+#define maxn 5005
+
+typedef pair<int, int> pii;
+
+pii a[maxn];
+
+int64_t dis(pii x, pii y) { return abs(x.first - y.first) + abs(x.second - y.second); }
+
+void solve(void) {
+    int n;
+    cin >> n;
+    for (int i = 1; i <= n; i++) cin >> a[i].first >> a[i].second;
+    vector<pii> answer;
+    while (true) {
+        bool chk = true;
+        for (int i = 2; i <= n; i++) chk &= (a[1] == a[i]);
+        if (chk) break;
+        int p = 2;
+        while (a[p] == a[1]) p++;
+        for (int i = p + 1; i <= n; i++)
+            if (a[1] != a[i] && dis(a[i], a[1]) < dis(a[p], a[1])) p = i;
+        if (a[1].first > a[p].first) swap(a[1], a[p]);
+        int tx = (a[1].first + a[p].first) / 2, ty = (a[1].second + a[p].second) / 2;
+        if (abs(a[1].first - tx) > abs(a[p].first - tx)) tx--;
+        if (abs(a[1].second - ty) < abs(a[p].second - ty)) ty += (ty < a[p].second ? +1 : -1);
+        int tot = min(abs(a[1].first - tx) + abs(a[1].second - ty), abs(a[p].first - tx) + abs(a[p].second - ty)) + 1;
+        for (int i = 1; i <= n; i++) {
+            int dx = abs(a[i].first - tx), dy = abs(a[i].second - ty), tim = tot;
+            if (tim >= dx)
+                a[i].first = tx, tim -= dx;
+            else
+                a[i].first += (a[i].first < tx ? +tim : -tim), tim = 0;
+            if (tim >= dy)
+                a[i].second = ty, tim -= dy;
+            else
+                a[i].second += (a[i].second < ty ? +tim : -tim), tim = 0;
+        }
+        answer.emplace_back(tx, ty);
+    }
+    cout << answer.size() << endl;
+    for (auto [x, y] : answer) cout << x << ' ' << y << endl;
+    return;
+}
+
+int main() {
+    ios::sync_with_stdio(false), cin.tie(nullptr), cout.tie(nullptr);
+
+    int _ = 1;
+    while (_--) solve();
+
+    return 0;
+}